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Table 8 The convergence performance and CPU time of the decoupled Algorithm  3.4 at time \(\pmb{T=1.0}\) , with varying time step Δ t but fixed mesh \(\pmb{h=\frac{1}{32}}\)

From: Stability and convergence of some novel decoupled schemes for the non-stationary Stokes-Darcy model

Δ t \(\boldsymbol {\frac{\|{\mathbf{u}}_{f}-{\mathbf{u}}^{m,h}_{3.4}\|_{0}}{\|{\mathbf{u}}_{f}\|_{0}}}\) \(\boldsymbol {\frac{\|{\mathbf{u}}_{f}-{\mathbf{u}}^{m,h}_{3.4}\|_{1}}{\|{\mathbf{u}}_{f}\|_{1}}}\) \(\boldsymbol {\frac{\|p_{f}-p^{m,h}_{3.4}\|_{0}}{\|p_{f}\|_{0}}}\) \(\boldsymbol {\frac{\|\phi-\phi^{m,h}_{3.4}\|_{0}}{\|\phi\|_{0}}}\) \(\boldsymbol {\frac{\|\phi-\phi^{m,h}_{3.4}\|_{1}}{\|\phi\|_{1}}}\) CPU(S)
0.1 0.00117118 0.0254554 0.117434 0.0154497 0.0405695 20.842
0.05 0.000953404 0.0254305 0.104073 0.00862193 0.0395156 42.126
0.025 0.000958537 0.0254216 0.0984034 0.00519615 0.0392372 83.936
0.0125 0.00102454 0.0254198 0.0973373 0.00349038 0.039165 172.19